Unpolarised light is incident on the boundary between two dielectric… | JEE Main 2023 (29 Jan, Shift 2)

Q39JEE Main 2023 · 29 JAN · SHIFT 2Medium

Polarisation

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium $-1$ ) and 6.8 (medium $-2$ ), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be $\tan^{-1}\left(1 + \frac{10}{\theta}\right)^{\frac{1}{2}}$ the value of $\theta$ is __________.

(Given for dielectric media, $\mu_r = 1$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 7

With $\mu_r = 1$ , refractive index $n = \sqrt{K}$ , so $\tan i_B = \frac{n_2}{n_1} = \left(\frac{6.8}{2.8}\right)^{1/2}$
$\frac{6.8}{2.8} = 1 + \frac{4}{2.8} = 1 + \frac{10}{7}$
Comparing with $\left(1 + \frac{10}{\theta}\right)^{1/2}$ gives $\theta = 7$ .

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